Q6. - Algebra 1

Question

The table below shows the relationship between certain temperatures in degrees Fahrenheit and degrees Celsius. Which of the following linear equations correctly models the relationship?  

 

Celsius (C)	Fahrenheit (F)
$10°$	$50°$
$15°$	$59°$
$20°$	$68°$
$25°$	$77°$
$30°$	$86°$

F $F=\frac{8}{5}C+35$

G $F=\frac{4}{5}C+42$

H $F=\frac{9}{5}C+32$

J $F=\frac{12}{5}C+26$

Step-by-Step Solution

Answer

The correct options are represented by H.

Step 1. Check the first option.

Take the first value of Celsius and substitute it into the equation provided in the first option to check whether it returns the corresponding Fahrenheit or not.

$$\begin{gathered} F=\frac{8}{5}\left(10\right)+35 \\ =16+35 \\ =51 \end{gathered}$$

As Fahrenheit is not equal to 50 so this option is incorrect.

Step 2. Check the second option.

Take the first value of Celsius and substitute it into the equation provided in second option to check whether it returns the corresponding Fahrenheit or not.

$$\begin{gathered} F=\frac{4}{5}\left(10\right)+42 \\ =8+42 \\ =50 \end{gathered}$$

Take the second value of Celsius and substitute it into the equation provided in second option to check whether it returns the corresponding Fahrenheit or not.

$$\begin{gathered} F=\frac{4}{5}\left(15\right)+42 \\ =12+42 \\ =54 \end{gathered}$$

As the Fahrenheit is not equal to 59 so this option is incorrect.

Step 3. Check the third option.

Take the first value of Celsius and substitute it into the equation provided in the third option to check whether it returns the corresponding Fahrenheit or not.

$$\begin{gathered} F=\frac{9}{5}\left(10\right)+32 \\ =18+32 \\ =50 \end{gathered}$$

Take the second value of Celsius and substitute it into the equation provided in the second option to check whether it returns the corresponding Fahrenheit or not.

$$\begin{gathered} F=\frac{9}{5}\left(15\right)+32 \\ =27+32 \\ =59 \end{gathered}$$

As Fahrenheit is equal to 59 so this option is correct.

Step 4. Check the fourth option.

Take the first value of Celsius and substitute it into the equation provided in the fourth option to check whether it returns the corresponding Fahrenheit or not.